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Diffstat (limited to 'src/hypot.c')
| -rw-r--r-- | src/hypot.c | 194 |
1 files changed, 194 insertions, 0 deletions
diff --git a/src/hypot.c b/src/hypot.c new file mode 100644 index 0000000..79e25ab --- /dev/null +++ b/src/hypot.c @@ -0,0 +1,194 @@ +/* mpfr_hypot -- Euclidean distance + +Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. +Contributed by the AriC and Caramel projects, INRIA. + +This file is part of the GNU MPFR Library. + +The GNU MPFR Library is free software; you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation; either version 3 of the License, or (at your +option) any later version. + +The GNU MPFR Library is distributed in the hope that it will be useful, but +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public +License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see +http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., +51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ + +#define MPFR_NEED_LONGLONG_H +#include "mpfr-impl.h" + +/* The computation of hypot of x and y is done by * + * hypot(x,y)= sqrt(x^2+y^2) = z */ + +int +mpfr_hypot (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd_mode) +{ + int inexact, exact; + mpfr_t t, te, ti; /* auxiliary variables */ + mpfr_prec_t N, Nz; /* size variables */ + mpfr_prec_t Nt; /* precision of the intermediary variable */ + mpfr_prec_t threshold; + mpfr_exp_t Ex, sh; + mpfr_uexp_t diff_exp; + + MPFR_SAVE_EXPO_DECL (expo); + MPFR_ZIV_DECL (loop); + MPFR_BLOCK_DECL (flags); + + MPFR_LOG_FUNC + (("x[%Pu]=%.*Rg y[%Pu]=%.*Rg rnd=%d", + mpfr_get_prec (x), mpfr_log_prec, x, + mpfr_get_prec (y), mpfr_log_prec, y, rnd_mode), + ("z[%Pu]=%.*Rg inexact=%d", + mpfr_get_prec (z), mpfr_log_prec, z, inexact)); + + /* particular cases */ + if (MPFR_ARE_SINGULAR (x, y)) + { + if (MPFR_IS_INF (x) || MPFR_IS_INF (y)) + { + /* Return +inf, even when the other number is NaN. */ + MPFR_SET_INF (z); + MPFR_SET_POS (z); + MPFR_RET (0); + } + else if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y)) + { + MPFR_SET_NAN (z); + MPFR_RET_NAN; + } + else if (MPFR_IS_ZERO (x)) + return mpfr_abs (z, y, rnd_mode); + else /* y is necessarily 0 */ + return mpfr_abs (z, x, rnd_mode); + } + + if (mpfr_cmpabs (x, y) < 0) + { + mpfr_srcptr u; + u = x; + x = y; + y = u; + } + + /* now |x| >= |y| */ + + Ex = MPFR_GET_EXP (x); + diff_exp = (mpfr_uexp_t) Ex - MPFR_GET_EXP (y); + + N = MPFR_PREC (x); /* Precision of input variable */ + Nz = MPFR_PREC (z); /* Precision of output variable */ + threshold = (MAX (N, Nz) + (rnd_mode == MPFR_RNDN ? 1 : 0)) << 1; + if (rnd_mode == MPFR_RNDA) + rnd_mode = MPFR_RNDU; /* since the result is positive, RNDA = RNDU */ + + /* Is |x| a suitable approximation to the precision Nz ? + (see algorithms.tex for explanations) */ + if (diff_exp > threshold) + /* result is |x| or |x|+ulp(|x|,Nz) */ + { + if (MPFR_UNLIKELY (rnd_mode == MPFR_RNDU)) + { + /* If z > abs(x), then it was already rounded up; otherwise + z = abs(x), and we need to add one ulp due to y. */ + if (mpfr_abs (z, x, rnd_mode) == 0) + mpfr_nexttoinf (z); + MPFR_RET (1); + } + else /* MPFR_RNDZ, MPFR_RNDD, MPFR_RNDN */ + { + if (MPFR_LIKELY (Nz >= N)) + { + mpfr_abs (z, x, rnd_mode); /* exact */ + MPFR_RET (-1); + } + else + { + MPFR_SET_EXP (z, Ex); + MPFR_SET_SIGN (z, 1); + MPFR_RNDRAW_GEN (inexact, z, MPFR_MANT (x), N, rnd_mode, 1, + goto addoneulp, + if (MPFR_UNLIKELY (++ MPFR_EXP (z) > + __gmpfr_emax)) + return mpfr_overflow (z, rnd_mode, 1); + ); + + if (MPFR_UNLIKELY (inexact == 0)) + inexact = -1; + MPFR_RET (inexact); + } + } + } + + /* General case */ + + N = MAX (MPFR_PREC (x), MPFR_PREC (y)); + + /* working precision */ + Nt = Nz + MPFR_INT_CEIL_LOG2 (Nz) + 4; + + mpfr_init2 (t, Nt); + mpfr_init2 (te, Nt); + mpfr_init2 (ti, Nt); + + MPFR_SAVE_EXPO_MARK (expo); + + /* Scale x and y to avoid overflow/underflow in x^2 and overflow in y^2 + (as |x| >= |y|). The scaling of y can underflow only when the target + precision is huge, otherwise the case would already have been handled + by the diff_exp > threshold code. */ + sh = mpfr_get_emax () / 2 - Ex - 1; + + MPFR_ZIV_INIT (loop, Nt); + for (;;) + { + mpfr_prec_t err; + + exact = mpfr_mul_2si (te, x, sh, MPFR_RNDZ); + exact |= mpfr_mul_2si (ti, y, sh, MPFR_RNDZ); + exact |= mpfr_sqr (te, te, MPFR_RNDZ); + /* Use fma in order to avoid underflow when diff_exp<=MPFR_EMAX_MAX-2 */ + exact |= mpfr_fma (t, ti, ti, te, MPFR_RNDZ); + exact |= mpfr_sqrt (t, t, MPFR_RNDZ); + + err = Nt < N ? 4 : 2; + if (MPFR_LIKELY (exact == 0 + || MPFR_CAN_ROUND (t, Nt-err, Nz, rnd_mode))) + break; + + MPFR_ZIV_NEXT (loop, Nt); + mpfr_set_prec (t, Nt); + mpfr_set_prec (te, Nt); + mpfr_set_prec (ti, Nt); + } + MPFR_ZIV_FREE (loop); + + MPFR_BLOCK (flags, inexact = mpfr_div_2si (z, t, sh, rnd_mode)); + MPFR_ASSERTD (exact == 0 || inexact != 0); + + mpfr_clear (t); + mpfr_clear (ti); + mpfr_clear (te); + + /* + exact inexact + 0 0 result is exact, ternary flag is 0 + 0 non zero t is exact, ternary flag given by inexact + 1 0 impossible (see above) + 1 non zero ternary flag given by inexact + */ + + MPFR_SAVE_EXPO_FREE (expo); + + if (MPFR_OVERFLOW (flags)) + mpfr_set_overflow (); + /* hypot(x,y) >= |x|, thus underflow is not possible. */ + + return mpfr_check_range (z, inexact, rnd_mode); +} |